Finite Group DatabasebetaFinite Group Databasebeta| order | 16002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×D127⋊C3 |
| Fitting, socle | C3×C7×C127 ⋊ C2×C3 |
| derived, Sylow | C127 ⋊ C2×C32×C7 |
| Hall | C3×C7×C127⋊C3 ⋊ C2 |
| Hall | C7×D127 ⋊ C32 |
| Hall | C3×C127⋊C3 ⋊ C2×C7 |
| Hall | C7×C127 ⋊ C2×C32 |
| Hall | D127 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D127⋊C3 |
| commutator, cosocle, hypocenter | C127 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C127 | C2×C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C3×C7 | |
48 conjugacy classes of subgroups.
567 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D7×D127⋊C3, D3×C7×D127⋊C3, D21×D127⋊C3, … |
| maximal normal subgroup of | C3×D7×D127⋊C3, D3×C7×D127⋊C3, D21×D127⋊C3, … |
| maximal quotient of | C3×C7×(C127⋊C3)⋊C4, C2×C3×C7×D127⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16002, 60);